Article: Digital Vinyl: Temporal Domain

[jabbr]

And the effect ultrasonics may have on the content in the audible spectrum is, of course, already included in the audible signal to begin with.

 

No. The effect of the ultrasonics would be on the nervous system to modulate the audible input to the nervous system.

 

There should be no assumption that there exists an equivalent purely audible signal that produces the same effect in the nervous system.

[Vincent1234]

And the effect ultrasonics may have on the content in the audible spectrum is, of course, already included in the audible signal to begin with.

The experiments I was talking about showed that including ultrasonics in the listening sessions (as opposed to excluding them) enhanced the 'naturalness' of the sound to the listeners.

 

Sent from my HTC One_M8 using Computer Audiophile mobile app

[esldude]

Maybe this would help too. Click to view animated GIF.

 

http://science-of-sound.net/wp-content/uploads/2016/02/TimeDomainResolution.gif

 

Notice how even though this waveform is shifted in time steps much smaller than the time of one sample period the waveform can be recreated even at in between steps. The reason is each shift makes the value of the samples change. There are likely many thousands of sample value combinations which will make this same exact wave form. But for each single combination of samples that create this waveform it only fits at one single instance in time. Move the waveform very slightly in time and a different combination of sample values creates the waveform at a different point in time. Remember that once you have 3 or more samples there is one and only one waveform at only one instance of time that will fit those sample point values. All other possibilities will fail to fit.

[board]

Yes and nice summary.

 

 

 

You would agree that if someone were to present a "properly" digitized 44.1 vs 96 or 192 or even DSD256 and your were able to detect an audible difference *and* assuming there is > 22 kHz info in the hi-res recording, then that would be evidence of ultrasonic effects on hearing?

 

Problem is definition of "properly" digitized. May not be easy.

 

Since the Nyquist sampling theorem show that the only difference between hi-res and CD quality is the extra amount of ultrasonics in the hi-res version, and no properly conducted study has so far shown that it's possible to distinguish the two, then a definition of "properly digitized", or at least "sufficient [in the sense of no more could make a difference]" would be 16/44.1. But of course, it should be a signal that was created with a good A/D converter that doesn't create aliasing, etc. Luckily, good A/D converters have become very cheap - even $50 soundblaster cards can be considered "sufficient", although if I was doing recordings I would definitely buy something better than that.

[jabbr]

Since the Nyquist sampling theorem show that the only difference between hi-res and CD quality is the extra amount of ultrasonics in the hi-res version, and no properly conducted study has so far shown that it's possible to distinguish the two, then a definition of "properly digitized", or at least "sufficient [in the sense of no more could make a difference]" would be 16/44.1. But of course, it should be a signal that was created with a good A/D converter that doesn't create aliasing, etc. Luckily, good A/D converters have become very cheap - even $50 soundblaster cards can be considered "sufficient", although if I was doing recordings I would definitely buy something better than that.

 

So then you would agree that demonstration of a consistent ability to distinguish between PCM44 and let's say DSD256 recordings would be proof of the ability to perceive ultrasonic content?

 

 

Room treatments for headphone users

[mansr]

So then you would agree that demonstration of a consistent ability to distinguish between PCM44 and let's say DSD256 recordings would be proof of the ability to perceive ultrasonic content?

 

No, it could be any of numerous minor differences.

[jabbr]

No, it could be any of numerous minor differences.

 

If one were doing a study it would be important to control for extraneous variables. I term that under "sufficient" ADC but he thought a $50 card would do. This is why the question is hard to answer definitively.

[Rt66indierock]

Assuming the ultrasonics we are discussing are created by musical instruments and are present when listening to live music, there is no reason to believe that these specific ultrasonics are harmful in any way. The very fact that you can perceive ultrasonics at all suggests that their absence from a recoding may form part of the difference between hearing the performance "live" vs "recorded".

 

I don't know anyone who gets headaches when listening up front and close to a quartet who likes classical music, same for jazz for people who like jazz. Perhaps its the ultrasonics which sends the "chill down your spine" when listening up front and close to live music?

 

Any ultrasonic sound has the same side effects whether it is music, dental equipment or some welders. In my case I could detect ultrasonic frequencies using a high frequency welder. If someone else was welding and I was observing I could not. Of course after reading James Boyk’s article (There’s Life Above 20 Kilohertz) I tried to recreate the effect on a drum kit and could detect some ultrasonic sound if I really hit the cymbal hard about 10 times. However trying to measure ultrasonic frequencies at any close listening positions or my favorite listening spots further back was elusive.

 

The presence or absence of ultrasonic frequencies has no effect on live vs. recorded because I listen to a lot of music without ultrasonic frequencies and the difference between live vs. recorded is just as great.

 

Music is harmful to hearing. I’ve had and have clients, friends and acquaintances DJs, recording engineers, musicians all have hearing loss.

 

As for headaches the worst were being too close to Buddy Rich in a club with my parents and an ELO concert in the front row. Consulting in the broadcasting industry (radio) was another day another headache. And of course audio shows. I went to two last year and with 85 dB average volume in the rooms it was like trying to get a headache. I use a program on my iPhone called Analyzer to position myself so I can enjoy live music at lower volumes.

 

Finally ultrasonic frequencies don’t cause the chill down your spine. How can you even think that? Read Chris’s review of the Nova 150 and David’s and my comments then consider these examples of music that gave me chills recently; J Geils Band “Give It to Me” Acoustic Version in my Miata, The Grateful Dead “Dead Set” about 1:20 on my iPod Shuffle with $15 Sony headphones getting ready for a long run, hearing the Honeycutters for the first time on my laptop computer and hearing Leonard Cohn’s Halleluiah in a mall Christmas shopping. No way is there ultrasonic frequencies in The Bands Brown Album from 1969 even though the equipment could reproduce them. And if you believe my Miata, cheap Sony headphone selected for comfort running, my HP Laptop and speakers in a mall can produce even 18kHz I have some desert land I’d like to show you.

[Le Concombre Masqué]

thank you, I truly appreciate your efforts and try hard to understand.

 

However as soon as your first paragraph I'm taken aback : a 1 khz sine wave is per definition periodical . That's my issue : bursts randomly emitted at high rate in a 20K bandwidth

Okay think of this. A 1 khz sine wave recorded by a microphone is changing all the time. 44.1 khz systems can sample and fully reconstruct that wave. If the recorded wave were 1 volt peak at peak maximum it will be 1 volt and one microsecond later it will be .99998 volts approximately. Our little 44.1 khz sample rate has managed to create this signal which is changing all the time. A continuously varying signal even at the smallest time intervals.

 

Now a constraint of discontinuously sampling a continuous waveform means above some frequency our sampling and reconstructing methods would not work correctly. So we are limited to a bit under half the sample rate. For all signals not filtered out however any possible waveform with no higher frequencies is reconstructed to change all the time. Even if the signal changes are in between samples even if new signals start or stop between samples.

 

In the case of our ears or microphones and such they also change continuously with the continuously changing waveform even at the smallest intervals of time. Due to the flexibility, weight, physical impedance to the air and damping our ear drums or microphone diaphragm at some high frequency will no longer couple to the air and can't change fast enough to mirror some part of the signal. They still change continuously, but for instance a 200,000 hz portion of the signal changes so fast our eardrums never move in response to that signal. So were it there in isolation or added to lower frequencies our ears drums aren't responding to it.

 

So if our discontinuously sampled digital recording has enough sample rate to record and reconstruct frequencies equal to or exceeding our ear's response higher frequencies will not matter even though filtered out. The signal that is reconstructed will vary rapidly enough our ear could not detect it any faster.

 

Maybe this helps instead of muddying the water.

[Le Concombre Masqué]

out of the blue... how 1/44 100 yields 1/(20000*2*pi*65536) deserves explanation and reference ; doesn't it?

You probably didn't see this, but I mentioned a few posts earlier that the calculation is not 1/44 100 second, but rather this: 1/(20000*2*pi*65536)

[esldude]

out of the blue... how 1/44 100 yields 1/(20000*2*pi*65536) deserves explanation and reference ; doesn't it?

 

There is a little mistake I think. Timing accuracy of digitally sampled audio is 1/(44,100*2*pi*65536) Works out to about 56 picoseconds. This is for 44,100 at 16 bit.

 

Imagine the 1 khz sine wave that varies value continuously as previously described. Now imagine I move it in time, but sample at the same time as previously. If I move it 1 picosecond the true value is different, but the difference is smaller than the Least significant bit which is the full scale divided by 65536 since that is how small 16 bits can encode. So it will encode as the very same sample value. Which is a little bit in error. Now if instead I move it 60 picoseconds, the difference in value at a given time while still very small is larger, and large enough it would change the sampled value by a minimum of the smallest bit value. Which will cause it to reconstruct at a different time upon playback.

 

Now if I went to 24 bits, the smallest change that will get captured by sampling is much smaller. Therefore smaller shifts in time will get captured that way instead of being missed. It would have time resolution of about .2 picoseconds. At least in a general way that is what that formula is about. The timing resolution is not the length of one sample period, but greatly smaller amounts of time.

[esldude]

thank you, I truly appreciate your efforts and try hard to understand.

 

However as soon as your first paragraph I'm taken aback : a 1 khz sine wave is per definition periodical . That's my issue : bursts randomly emitted at high rate in a 20K bandwidth

 

Well I was trying to make it understandable by keeping it simple at first. I hoped the latter paragraphs would illuminate a bit more. I don't know perhaps a good explanation if the graphic earlier didn't help. Bursts randomly emitted as long as the content is below 20 khz will get captured and properly reconstructed included the beginning or ending of a burst that occurs in between sample points. Remember there is one and only one waveform that will fit the samples. Also remember that any waveform can be created from a combination of sine waves. Sine waves may be added or stop or shifted in time to make some complex varying signal like bursts from a trumpet being played, but any waveform that is possible to occur can be created by some combination of sine waves and all of those can be sampled and combined in digital audio so they can be reconstructed even though they seem terribly complex and non-uniform.

 

So imagine I have my 1 khz sine wave going and suddenly add a 440 hz C note that starts, grows in level rapidly and then decays to disappear. It will get captured and sampled and only one set of samples fit and it will get reconstructed just like it happened within the parameters of the sample rate and bit depth. The speed at which that occurs is not a problem nor the precise timing as long as content above 20 khz is filtered out.

 

Is this helping or not? If not just say so. I am not good at explaining things. Probably others could do better. Maybe at least it will bring forth more questions which can be answered in a way that helps you.

[jabbr]

However as soon as your first paragraph I'm taken aback : a 1 khz sine wave is per definition periodical . That's my issue : bursts randomly emitted at high rate in a 20K bandwidth

 

If the bursts are randomly emitted at a "high rate" then they either are or aren't within the 20k bandwidth. If they can't be captured within 44100 Hz sampling rate then they, by definition, reflect frequencies > 21 kHz.

[jabbr]

Any ultrasonic sound has the same side effects whether it is music, dental equipment or some welders. In my case I could detect ultrasonic frequencies using a high frequency welder....

The presence or absence of ultrasonic frequencies has no effect on live vs. recorded because I listen to a lot of music without ultrasonic frequencies and the difference between live vs. recorded is just as great.

...Music is harmful to hearing. I’ve had and have clients, friends and acquaintances DJs, recording engineers, musicians all have hearing loss.

 

As for headaches the worst were being too close to Buddy Rich in a club with my parents and an ELO concert in the front row. Consulting in the broadcasting industry (radio) was another day another headache. And of course audio shows. I went to two last year and with 85 dB average volume in the rooms it was like trying to get a headache. I use a program on my iPhone called Analyzer to position myself so I can enjoy live music at lower volumes.

...Finally ultrasonic frequencies don’t cause the chill down your spine. How can you even think that? Read Chris’s review of the Nova 150 and David’s and my comments then consider these examples of music that gave me chills recently; J Geils Band “Give It to Me” Acoustic Version in my Miata, The Grateful Dead “Dead Set” about 1:20 on my iPod Shuffle with $15 Sony headphones getting ready for a long run, hearing the Honeycutters for the first time on my laptop computer and hearing Leonard Cohn’s Halleluiah in a mall Christmas shopping.

Two things:

 

1) Music preference is individual and the response to ultrasonics might also be individual. In any case your own responses to music are very unlikely to reflect mine. The musicians I know best don't have hearing loss even though playing for decades but they are classical musicians.

 

2) The sensation of "live" music likely is composed of multiple factors which we only partly or even poorly understand. To use your example, if we were attempting to replay a J. Geils recording "like live" there would be factors different from attempting to replay a quartet recording "like live". The Grateful Dead engineers spent a considerable amount of thought on amplification equipment, so another difference there. Memory also plays a role etc.

 

I don't think all of this is merely "ultrasonics", certainly dynamic range but likely other factors that aren't even widely discussed. I do think that bone conduction as well as tactile stimuli may play a role e.g. low bass that you can "feel".

[mansr]

Well I was trying to make it understandable by keeping it simple at first. I hoped the latter paragraphs would illuminate a bit more. I don't know perhaps a good explanation if the graphic earlier didn't help. Bursts randomly emitted as long as the content is below 20 khz will get captured and properly reconstructed included the beginning or ending of a burst that occurs in between sample points. Remember there is one and only one waveform that will fit the samples. Also remember that any waveform can be created from a combination of sine waves. Sine waves may be added or stop or shifted in time to make some complex varying signal like bursts from a trumpet being played, but any waveform that is possible to occur can be created by some combination of sine waves and all of those can be sampled and combined in digital audio so they can be reconstructed even though they seem terribly complex and non-uniform.

 

So imagine I have my 1 khz sine wave going and suddenly add a 440 hz C note that starts, grows in level rapidly and then decays to disappear. It will get captured and sampled and only one set of samples fit and it will get reconstructed just like it happened within the parameters of the sample rate and bit depth. The speed at which that occurs is not a problem nor the precise timing as long as content above 20 khz is filtered out.

 

Is this helping or not? If not just say so. I am not good at explaining things. Probably others could do better. Maybe at least it will bring forth more questions which can be answered in a way that helps you.

 

Bear in mind that suddenly starting or stopping a sine wave, even a low-frequency one, and even if done at a zero crossing, introduces a discontinuity in the first differential which amounts to a wideband burst. The same is true for any sharp corner in the waveform.

[Jud]

Bear in mind that suddenly starting or stopping a sine wave, even a low-frequency one, and even if done at a zero crossing, introduces a discontinuity in the first differential which amounts to a wideband burst. The same is true for any sharp corner in the waveform.

 

https://en.wikipedia.org/wiki/Gibbs_phenomenon

[The Computer Audiophile]

Hi Guys - So if I understand this correctly, Monty is directly refuting the premise of this article, starting at 20:53?

 

[video=youtube_share;cIQ9IXSUzuM]

[Don Hills]

Hi Guys - So if I understand this correctly, Monty is directly refuting the premise of this article, starting at 20:53? ...

 

Indeed. He shows a transient event, in this case a "leading edge" of a square wave signal, being sampled (A to D) while the time the transient occurs is varied between sampling periods.

 

Edit: If anyone wonders why the transient has a "slope" instead of being nice and "vertical", he shows earlier in the video how a square wave is composed of sine waves with their frequencies theoretically extending to infinity. When you filter out all the frequencies above Nyquist as required by the sampling theorem, you're left with exactly what you see onscreen.

[esldude]

Bear in mind that suddenly starting or stopping a sine wave, even a low-frequency one, and even if done at a zero crossing, introduces a discontinuity in the first differential which amounts to a wideband burst. The same is true for any sharp corner in the waveform.

 

Yes, yes, all true. I was keeping it simple not trying to gloss over deficiencies in sampled waveforms.

[esldude]

Hi Guys - So if I understand this correctly, Monty is directly refuting the premise of this article, starting at 20:53?

 

[video=youtube_share;cIQ9IXSUzuM]

 

Yes that among other things shown in the video is why I have it in my signature. Why I have said at least once or more that so many of these ridiculous arguments about what digital can and cannot do would be avoided if everyone commenting would watch and take time to understand that 23 minute video.

 

Possibly number one is the idea repeated millions of times that digital audio loses whatever happens, starts or stops between the sample points. Yet the video demonstrated that as NOT so. And did so with analog inputs and analog monitored outputs.

 

So you get these articles like this about LP being better at timing that digital just can't touch, and it is demonstrably wrong and way off base. If your number one beginning premise is so wrong, everything that follows from it is highly suspect, and usually going to be wrong. Which is why I was dismayed to see you give home page space to this article.

 

If temporal resolution is as important as Pure Vinyl thinks, then digital is the way to go for sure.

 

Pure Vinyl had this image in the article to illustrate the steep transients that digital can't catch implying a vertical ramp up to impulsive signals:

 

It depends upon how close you look. Here is the plot of an actual cymbal recording at 176 khz, using a wide bandwidth Earthworks microphone. This cymbal is one of the quickest most impulsive available. It too looks nearly full vertical on the leading edge.

 

But looks closer:

 

And closer still you see it was not so vertical nor so steep that it can't be sampled. This is far steeper than you will normally see in any music except rarely.

 

Most musical instruments including cymbals are resonant devices. Even steep impulsive hits take a few cycles to ramp up to full level. Hit a cymbal and it takes time for the energy to travel over the metal surface and be reflected back to resonate. Just as in rooms at low frequencies room resonance doesn't reach full value in one cycle. Plucked strings are in front of a resonant box and also don't instantly reach max value though I think people have this picture in their mind.

[Jud]

Yes that among other things shown in the video is why I have it in my signature. Why I have said at least once or more that so many of these ridiculous arguments about what digital can and cannot do would be avoided if everyone commenting would watch and take time to understand that 23 minute video.

 

Possibly number one is the idea repeated millions of times that digital audio loses whatever happens, starts or stops between the sample points. Yet the video demonstrated that as NOT so. And did so with analog inputs and analog monitored outputs.

 

So you get these articles like this about LP being better at timing that digital just can't touch, and it is demonstrably wrong and way off base. If your number one beginning premise is so wrong, everything that follows from it is highly suspect, and usually going to be wrong. Which is why I was dismayed to see you give home page space to this article.

 

If temporal resolution is as important as Pure Vinyl thinks, then digital is the way to go for sure.

 

Pure Vinyl had this image in the article to illustrate the steep transients that digital can't catch implying a vertical ramp up to impulsive signals:

[ATTACH=CONFIG]34032[/ATTACH]

 

It depends upon how close you look. Here is the plot of an actual cymbal recording at 176 khz, using a wide bandwidth Earthworks microphone. This cymbal is one of the quickest most impulsive available. It too looks nearly full vertical on the leading edge.

[ATTACH=CONFIG]34033[/ATTACH]

 

But looks closer:

[ATTACH=CONFIG]34034[/ATTACH]

 

And closer still you see it was not so vertical nor so steep that it can't be sampled. This is far steeper than you will normally see in any music except rarely.

[ATTACH=CONFIG]34035[/ATTACH]

 

Most musical instruments including cymbals are resonant devices. Even steep impulsive hits take a few cycles to ramp up to full level. Hit a cymbal and it takes time for the energy to travel over the metal surface and be reflected back to resonate. Just as in rooms at low frequencies room resonance doesn't reach full value in one cycle. Plucked strings are in front of a resonant box and also don't instantly reach max value though I think people have this picture in their mind.

 

Are you able to convert to 44.1kHz and show what it looks like there?

 

 

Sent from my iPhone using Computer Audiophile

[esldude]

Are you able to convert to 44.1kHz and show what it looks like there?

 

 

Sent from my iPhone using Computer Audiophile

 

I sample rate converted to 44.1 and then back to 176 so the scale would match on both. Upper is the original 176 khz and lower is the 44 khz.

 

 

 

 

 

You can see in the latter image that the very beginning of the transient wasn't slow to start on 44 khz. You do see some peaks are rounded and lower in level due to the energy in ultrasonic frequencies that were not captured.

 

It is hard to say where the real fundamental modes of the cymbal are. The decaying tail has strong output at 6700 hz and 8 khz with a big drop off after that. The harmonics do extend to maybe 50 khz prior to 100 milliseconds. The microphone used is said flat to 40 khz and I am sure has some output beyond that. After about 100 milliseconds the strong harmonics beyond 10 khz suddenly die out leaving pretty much only below 10 khz sound.

 

Here is the spectrogram. It goes to the gray background at -80 db and uses 1024 bin FFT as I have it set here.

 

[esldude]

Okay here is the spectrogram only showing one channel which gives me more room so you can see more details.

 

 

If I do a steep brickwall filter at 20 khz the first 100 milliseconds averages RMS levels of -20.6 db full range and -21.0 after filtering out the ultrasonics. The 44.1 khz file after being upconverted also shows -21 db for the same time period.

[Le Concombre Masqué]

Hope I won't ruin your patience but I'm getting more and more confused :

 

to my understanding every demo and thus SN theorem relies on both the band limitation and the periodical nature of the signal, the 2 (X2, twice bandwidth) factor being related to the fact that, taking into account the given sinusoidal shape by nature of the signal, what was up will be mirrored down, that there's only one solution for a given position at a determined timing in a limited bandwidth.

 

This is why I tried to break the image by bursts at rates higher than sampling.

 

Led to out of bandwidth.

 

We now are looking at signals that when recorded at 176 yield degraded versions at 44.

 

So, at the end of the day (actually very beginning here !) is 44 perfectly enough as per Monty etc or do actual sound emissions require larger bandwidth for better capture and can this capture be accurately be reproduced at 44? To my eyes you demonstrate Yes they require larger bandwidth, No 44 can not be faithful.

 

I'm confused for it would thus appear that if it's not a matter of number of samples it's a matter of bandwidth ; isn't it silly ?

 

I understand the desire to share the beauty of the sampling theorem and how misconceived is the idea of non accuracy that would come from steps and presumed losses that don't occur ; but at the end of the day, seems that actual signals require big bandwidth hence bigger sampling rates, not because of out of audible band but to catch quick impulses.

 

 

This being said, I sometimes don't hear a difference or generally prefer 192 downloads but would not fight much for it while I'll take the risk to claim I'm a big (Monty's dismissed) 24 fan.

 

What about 24 ? There's the 16 good enough S/N, the magical dither, the out of need timing accuracy improvement at sampling level ; yet it sounds better to my ears and my brain likes the idea of more precisely measured steps though I read it's not needed nor working like that but rather towards a studio mixing only requirement

 

thank you

 

 

I sample rate converted to 44.1 and then back to 176 so the scale would match on both. Upper is the original 176 khz and lower is the 44 khz.

 

[ATTACH=CONFIG]34044[/ATTACH]

 

 

[ATTACH=CONFIG]34045[/ATTACH]

 

 

You can see in the latter image that the very beginning of the transient wasn't slow to start on 44 khz. You do see some peaks are rounded and lower in level due to the energy in ultrasonic frequencies that were not captured.

 

It is hard to say where the real fundamental modes of the cymbal are. The decaying tail has strong output at 6700 hz and 8 khz with a big drop off after that. The harmonics do extend to maybe 50 khz prior to 100 milliseconds. The microphone used is said flat to 40 khz and I am sure has some output beyond that. After about 100 milliseconds the strong harmonics beyond 10 khz suddenly die out leaving pretty much only below 10 khz sound.

 

Here is the spectrogram. It goes to the gray background at -80 db and uses 1024 bin FFT as I have it set here.

 

[ATTACH=CONFIG]34046[/ATTACH]

[esldude]

Hope I won't ruin your patience but I'm getting more and more confused :

 

to my understanding every demo and thus SN theorem relies on both the band limitation and the periodical nature of the signal, the 2 (X2, twice bandwidth) factor being related to the fact that, taking into account the given sinusoidal shape by nature of the signal, what was up will be mirrored down, that there's only one solution for a given position at a determined timing in a limited bandwidth.

 

This is why I tried to break the image by bursts at rates higher than sampling.

 

Led to out of bandwidth.

 

We now are looking at signals that when recorded at 176 yield degraded versions at 44.

 

So, at the end of the day (actually very beginning here !) is 44 perfectly enough as per Monty etc or do actual sound emissions require larger bandwidth for better capture and can this capture be accurately be reproduced at 44? To my eyes you demonstrate Yes they require larger bandwidth, No 44 can not be faithful.

 

I'm confused for it would thus appear that if it's not a matter of number of samples it's a matter of bandwidth ; isn't it silly ?

 

I understand the desire to share the beauty of the sampling theorem and how misconceived is the idea of non accuracy that would come from steps and presumed losses that don't occur ; but at the end of the day, seems that actual signals require big bandwidth hence bigger sampling rates, not because of out of audible band but to catch quick impulses.

 

 

This being said, I sometimes don't hear a difference or generally prefer 192 downloads but would not fight much for it while I'll take the risk to claim I'm a big (Monty's dismissed) 24 fan.

 

What about 24 ? There's the 16 good enough S/N, the magical dither, the out of need timing accuracy improvement at sampling level ; yet it sounds better to my ears and my brain likes the idea of more precisely measured steps though I read it's not needed nor working like that but rather towards a studio mixing only requirement

 

thank you

 

Okay in a perfect world with perfect reconstruction higher sampling rates get you higher bandwidth. They do get you better time resolution, but it is already so good that should not matter by a factor of like several hundred times at least. So you get bandwidth. You don't get a more accurate reconstruction of the signal below 20 khz. In the above example the differences you see are from no bandwidth above 20 khz at the 44.1 khz sample rate.

 

Now yes there is some signal above 20 khz. Can you hear it, does it effect the sound your ears hear if it is gone versus if it is present? I don't think so. People typically can't hear the difference unsighted. Our basilar membrane in the ear has a physical construction that appears to end response at 15 or 16 khz. It acts as a loosely tuned filter at that point with some rapidly diminishing response above that frequency which is why with enough sound level you can hear 20 khz when young. A small percentage of people with the most excellent hearing in their 20's can hear 23 khz. Now I don't know the answer, I bet at least when young the ear drum probably responds up a bit more, but the basilar membrane which is what activates the auditory nerve responds weakly if at all up around 20 khz.

 

Below is a comparison of a cochlea mathematical model vs actual results. It gets pretty close. Notice the peak somewhere around 16 khz and then around 20 khz it simply drops to no response.

 

 

Using that same model this page has animation of the BM response in the cochlea for several types of signals. One of those is a Dirac impulse. Click on that circle for the 'pulse sequence' and see what is predicted.

 

Traveling Waves

 

 

Bone conduction can stimulate some sense at higher frequencies. Sounds through the air are not energizing bone anywhere close to enough to matter unless sound level reached more than 150 db. You would be deafened by everything else if that happened and still not hear it. The BM stereocilia would be destroyed or highly damaged.

 

So that leaves imperfect implementation of our digital system. It is my opinion that is close enough to theory it is of no concern. Others feel differently. I would note that is feel differently.

 

I know it is a cliche. If you sit someone down and show them SD and HDTV there is no question which is better. Super plain and simple. Ditto for 4k TV. If there is some benefit to higher sample rates it is a very small benefit nowhere near the differences in TV resolutions. If it were half that large we would not have any argument whatsoever at this late date.

 

If you still want to go higher rate just in case, I certainly see no reason for more than 96 khz. I mean you aren't hearing 40 khz or artefacts from that even if instruments have some harmonics higher than that. Damned few microphones go even to 40 khz. Anything which has gone across tape is diminished up there. I see no basis for 192, 384 and more.

 

Now you mention catching quick impulses. Even when an impulse is quick your ear simply has no pathway to follow it fully. Higher harmonics are going to be filtered out just the same. The upper filter is pretty steep on your ear too. That is why some DACs don't sound tremendously awful if they don't have a reconstruction filter. The roll off of ear response IS the filter.

 

So I couldn't say with 100% certainty 44.1 khz is enough or even 48 khz. There are lots of reasons, not opinions, but well founded reasons to think it is. To think if something is missed it is either of no consequence or something so small as to be of highly limited difference in terms of how satisfying the playback is for you.

 

As for 16 or 24 bits you could make a case for either way. 16 bit isn't losing much though there are cases where it could be audible. Much more so than higher sample rates. Basically with modern gear go 24 and don't worry about it. Then again with modern popular music compression is so out of hand dithered 8 bit is good enough. What little hiss you might get would give that old cassette softness which might cover up some of the spitty sound of limiting kicking in.